My TL2 is not 3.03" spindle bore, it is not even 3.00" spindle bore. As near as I can measure it is something like 2.95"; certainly 3" diameter material will not enter.
Your HFO must be looking in the wrong places. I have both 8" and 10" (Bison I think) three jaw chucks each with its own mounting plate.
I think 12" is a bit big. The inertia of that size will certainly mean the spindle takes a lot more time to start and stop, and the machine is not powerful enough to fully utilize the holding diameter of a 12".